Lectures related to Iterative Methods for Linear Equations

Introduces iterative methods for solving linear equations and discusses the gradient method for minimizing errors.

Explains the Jacobi and Gauss-Seidel methods for solving linear systems iteratively.

Covers the analysis of linear systems, focusing on methods such as Jacobi and Richardson for solving linear equations.

Covers the Crank-Nicolson and Heun's methods, discussing uniqueness of solutions and truncation errors in numerical methods.

Newton's Method: Convergence and Criteria

Explores the Newton method for non-linear equations, discussing convergence criteria and stopping conditions.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Numerical Methods: Euler and Crank-Nicolson

Covers Euler and Crank-Nicolson methods for solving differential equations.

Direct and Iterative Methods for Linear Equations

Explores direct and iterative methods for solving linear equations, emphasizing symmetric matrices and computational cost.

Newton's Method: Order 2

Explains Newton's method of order 2 for finding function zeros.

Linear Systems: Convergence and Methods

Explores linear systems, convergence, and solving methods with a focus on CPU time and memory requirements.

Linear Systems: Iterative Methods

Covers iterative methods for solving linear systems, including Jacobi and Gauss-Seidel methods.

Convergence of Fixed Point Methods

Explores the convergence of fixed point methods and the implications of different convergence rates.

Conjugate Gradient Method: Iterative Optimization

Covers the conjugate gradient method, stopping criteria, and convergence properties in iterative optimization.

Iterative Methods for Linear Equations

Explores iterative methods for linear equations, including Jacobi and Gauss-Seidel methods, convergence criteria, and the conjugate gradient method.

Linear Systems: Iterative Methods

Explores linear systems and iterative methods like gradient descent and conjugate gradient for efficient solutions.

Numerics: semester project

Covers the semester project on numerics, focusing on adaptive algorithms and multistep methods.

Linear Systems: Richardson's Method

Covers Richardson's method for solving linear equations and its applications in system solutions and error control.

Finite Elements Method: Error Estimation

Explores a priori error estimation in the finite elements method, covering convergence analysis, orthogonality, weak formulations, and optimal precision.

Convergence Analysis: Iterative Methods

Covers the convergence analysis of iterative methods and the conditions for convergence.